Flexible meshing type gear device with a passing tooth profile

ABSTRACT

In a meshing type gear device (1), spur gears are used for both a rigid internal gear (2) and a flexible external gear (3), and the number of teeth of the flexible gear (3) is made greater by two than that of the rigid internal gear (2). The tooth profile of the flexible external gear (3) is made convex and the shape thereof is that of a curve AC obtained by subjecting a gear tooth portion (curve portion between A and B), which, at the moving path L that the external gear describes relative to the internal gear, as determined by rack approximation, is convex relative to the internal gear, to similarity transformation at a reduction ratio λ using the limiting point A of the contact between the two gears on the path as the origin, while the tooth profile of the rigid internal gear is made concave and the shape thereof is that of a curve AD obtained by subjecting the same portion convex relative to the internal gear at the moving path to similarity transformation at an enlargement ratio (1+λ) using the limiting point A as the origin, whereby the meshing of the two gears maintains continuous contact and is of the passing type.

TECHNICAL FIELD

This invention relates to a flexible meshing type gear device. Moreparticularly, this invention relates to the tooth profiles of a rigidinternal gear and a flexible external gear used in a flexible meshingtype gear device.

BACKGROUND ART

A flexible meshing type gear device typically consists of a rigidcircular internal gear, a flexible external gear which has, for example,2 n (n being a positive integer) fewer teeth than the internal gear andwhich is disposed inside the internal gear and flexed into an ellipticalshape so as to mesh with the internal gear at two places, and a wavegenerator fitted inside the external gear for flexing it into anelliptical shape.

Although the basic tooth profile for the gears of a flexible meshingtype gear device is linear (see U.S. Pat. No. 2,906,143), flexiblemeshing type gear devices using involute gears have also been developed(see JP-B 45-41171). In addition, for increasing device load capacitythe present inventor proposed a system using as the tooth face profileof both gears the curve obtained by similarity transforming the movingpath, at a reduction ratio of 1/2, over a prescribed range from themeshing limit point on the path based on the rack approximation of thetooth of the external gear relative to the internal gear (JP-A63-115943). This is a system for obtaining continuous contact betweenthe tooth profiles of the tooth faces of both gears.

There is known a flexible meshing type gear device of a type fitted witha cup-shaped flexible external gear. In this type of device, athree-dimensional phenomenon called coning occurs in which the insertionof the elliptical wave generator causes the amount of flexing(difference between the major and minor axes of the ellipse) togradually increase from the diaphragm side toward the opening portion ofthe cup-shaped flexible external gear approximately in proportion to thedistance from the diaphragm. The tooth profiles described in theaforementioned publications do not take this coning into consideration,however. Therefore, while continuous meshing of the tooth profiles ofthe two gears can be realized for tooth traces with specific sections(e.g., a non-deviated section corresponding to the normal amount offlexing), tooth interference and other problems arise for other sectionsof the tooth trace.

The inventor later proposed a flexible meshing type gear device enablinga wider mesh range, without interference, over the entire tooth trace ofthe cup-shaped flexible external gear. This device is proposed, forexample, in Japanese Patent Applications Hei 3-357036 and Hei 3-357037.

The performance being demanded of flexible meshing type gear devices isbecoming increasingly sophisticated. To respond to this demand, it isnecessary to further improve device strength and wear resistance. Thereis a particular need to improve the wear resistance of the tooth surfaceto the maximum possible.

All of the aforementioned inventions enable continuous meshing along thetooth trace. However, the meshing is so-called countermovement meshing.Since it is therefore impossible to avoid disadvantages from the pointof maintaining a lubricating oil film between the tooth surfaces, acertain limit on the permissible delivered torque is present owing totooth surface wear caused by oil film rupture. Because of this, a strongneed is felt for an improvement in this respect.

DISCLOSURE OF THE INVENTION

For achieving the aforesaid improvement, this invention undertakes tochange the both convex tooth profiles performing countermovement meshingto convex and concave tooth profiles performing pass meshing, proposes atooth-number reversal method described later, and derives the toothprofile from a moving path with reverse phase.

More specifically, this invention is characterized in that the followingconfiguration is adopted in a flexible meshing type gear device having arigid internal gear, a flexible external gear inside the internal gearand a wave generator for flexing the external gear into an ellipticalcross-sectional shape, causing the external gear to mesh partially withthe rigid internal gear and rotating the mesh position of the two gearsin the circumferential direction, the rotation of the wave generatorproducing relative rotation between the two gears.

(a) The rigid internal gear and the flexible external gear are both spurgears.

(b) The number of teeth of the flexible external gear is two greaterthan that of the rigid internal gear.

(c) The tooth profile of the flexible external gear is convex and theshape thereof is that of a curve obtained by subjecting a gear toothportion, which, at the moving path that the external gear describesrelative to the internal gear, as determined by rack approximation, isconvex relative to the internal gear, to similarity transformation at areduction ratio λ using the limiting point of the contact between thetwo gears on the path as the origin.

(d) The tooth profile of the rigid internal gear is concave and theshape thereof is that of a curve obtained by subjecting the same portionconvex relative to the internal gear at the moving path to similaritytransformation at an enlargement ratio (1+λ) using the limiting point asthe origin, whereby the meshing of the two gears maintains continuouscontact and is of the passing type.

On the other hand, this invention is characterized in that the followingconfiguration is adopted in a flexible meshing type gear device equippedwith a cup-shaped flexible external gear.

(a) The rigid internal gear and the cup-shaped flexible external gearare both spur gears.

(b) The number of teeth of the cup-shaped flexible external gear is twogreater than that of the rigid internal gear.

(c) The tooth profile of the cup-shaped flexible external gear is convexand the shape thereof is that of a curve obtained by subjecting a geartooth portion which, at the moving path that the external gear describesrelative to the internal gear in a basic section of the tooth trace, asdetermined by rack approximation, is convex relative to the internalgear to similarity transformation at a reduction ratio λ using thelimiting point of the contact between the two gears on the path as theorigin.

(d) The tooth profile of the rigid internal gear is concave and theshape thereof is that of a curve obtained by subjecting the same portionconvex relative to the internal gear at the moving path to similaritytransformation at an enlargement ratio (1+λ) using the limiting point asthe origin, whereby the meshing of the two gears maintains continuouscontact and is of the passing type.

(e) Relieving is applied to teeth of the cup-shaped flexible externalgear toward the opening side from the basic section of the tooth trace.

In order to further expand the meshing region of the two gears, it ispreferable, in addition to the above feature (e), to apply reverserelieving to teeth of the cup-shaped flexible external gear toward thediaphragm side from the basic section of the tooth trace.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a perspective view of a flexible meshing type gear deviceequipped with a cup-shaped flexible external gear.

FIG. 2 is a schematic front view of the device of FIG. 1.

FIG. 3 is a set of diagrams for explaining how the cup-shaped flexibleexternal gear is flexed by coning, in which (a) is section through theaxis before deformation, (b) is a section through the axis including themajor axis of the wave generator, and (c) is a section through the axisincluding the minor axis.

FIG. 4 is the moving path in a basic section perpendicular to the axisin the case of negative deviation of a tooth of the cup-shaped flexibleexternal gear relative to the rigid internal gear in a flexible meshingtype gear device.

FIG. 5 is a diagram for explaining the method of tooth profilederivation of this invention.

FIG. 6 is a diagram for explaining the meshing of conventionalcountermovement type tooth profiles.

FIG. 7 is an explanatory diagram of the meshing of the tooth profiles ofthis invention in a basic section perpendicular to the tooth, drawnrelatively with respect to one tooth space of the rigid internal gearfollowed over the passage of time.

FIG. 8 is an explanatory diagram of the meshing of the tooth profiles ofthis invention in a basic section perpendicular to the tooth, drawnspatially over half the teeth of the rigid internal gear.

FIG. 9 is a set of diagrams for explaining meshing of the tooth profilesof this invention in basic sections other than that perpendicular to thetooth, in which (a) is for a section on the opening side of the basicsection perpendicular to the tooth, (b) shows the case of applyingrelieving thereto, (c) is for a section on the diaphragm side of thebasic section perpendicular to the tooth, and (d) shows the case ofapplying reverse relieving thereto.

FIG. 10 is a set of diagrams for explaining correction applied to theteeth of the cup-shaped flexible external gear, in which (a) is adiagram showing relieving applied on the opening side of a basic sectionperpendicular to the tooth and (b) is a diagram showing reverserelieving further applied on the diaphragm side of the basic sectionperpendicular to the tooth.

BEST MODE FOR CARRYING OUT THE INVENTION

Embodiments of the invention will be explained with reference to thedrawings in the following.

FIGS. 1 and 2 are perspective and front views of a prior-art flexiblemeshing type gear device to which this invention can be applied. Thisflexible meshing type gear device 1 comprises a cylindrical rigidinternal gear 2, a cup-shaped flexible external gear 3 disposed insidethe rigid internal gear 2, and a elliptical wave generator 4 fittedinside the cup-shaped flexible external gear 3. The cup-shaped flexibleexternal gear 3 is in a flexed state produced by the wave generator 4.

FIG. 3 shows the flexed state in sections through the axis of thecup-shaped flexible external gear 3 caused so-called coning, namely, byflexing the opening portion of the flexible external gear. FIG. 3(a)shows the state before deformation, (b) is a section through the axisincluding the major axis of the wave generator 4, and (c) is a sectionthrough the axis including the minor axis thereof. As can be seen fromthese diagrams, the amount of flexing produced in the cup-shapedflexible external gear 3 is maximum at the opening portion 3a andgradually decreases toward the side of a diaphragm 3b.

The point in which this invention differs fundamentally from prior-artflexible meshing type gear devices is that the number of teeth of theflexible external gear is two greater than that of the rigid internalgear. Since the difference in number of teeth is reversed from inprior-art devices in this way, the moving path of the flexible externalgear to which this invention is applied becomes as shown in FIG. 4.

More specifically, FIG. 4 shows the moving path L of a tooth of thecup-shaped flexible external gear with respect to the rigid internalgear in a basic section perpendicular to the tooth of the flexibleexternal gear (a section perpendicular to the axis for considering themoving path used to derive the tooth profile; normally taken as thesection at the center of the tooth trace) in the case where the amountof flexing (difference between the major and minor axes of the ellipseproduced by deformation of the pitch circle of the flexible externalgear) is κ (κ<1) times the normal value d, i.e., κd. This is theso-called negative deflection state. The phase is inverted verticallyfrom that of the moving path of the external gear in prior-art devicesof this type.

Since a flexible meshing type gear device has many teeth, the meshingcan be approximated as a rack. In this and the other drawings,therefore, it is treated by rack approximation.

FIG. 5 is a diagram for explaining the method of tooth profilederivation of this invention. Point A is the upper (deeper in the toothspace of the rigid internal gear) limiting point of meshing on themoving path L. Point B is the lower limiting point of the curved portionof the path which is convex with respect to the rigid internal gear.Curve AC is obtained by similarity transformation (a proportional sizechange) of the original curve of the moving path between A and B at areduction ratio λ using point A as the origin (center of similarity) andthis curve AC is adopted as the tooth profile of the flexible externalgear. This tooth profile is therefore convex.

Next, curve AD is obtained by similarity transformation of curve AB atan enlargement ratio (1+λ) using point A as the origin and this curve ADis adopted as the tooth profile of the rigid internal gear. This toothprofile is therefore concave. Here, point B is defined beforehand withinthe range in which intersection with the tooth profile on the oppositeside does not occur.

Since the foregoing alone results in a flexible external gear tooth thatcomes to a point at the tip, in actual practice the tooth is somewhatlowered and has a tooth crest at the top, as shown in the drawing.

That the two gears properly mesh can be demonstrated as follows.

Define an arbitrary point on the tooth profile AD of the rigid internalgear as R and draw straight line AR. Let the points of intersection ofstraight line AR with the tooth profile AC of the flexible external gearand the moving path AB be P and Q. In view of the manner in which thetooth profile was determined, it then holds that

    AP=λ.AQ

    AR=(1+λ).AQ.

Therefore,

    QR=AR-AQ=λ.AQ=AP.

From the nature of similarity, moreover, the tangents to the curves atthe three points P, Q and R are mutually parallel.

From these two facts, it can be seen that when point A of the convextooth profile AC is at point Q, the convex tooth profile AC contacts theconcave tooth profile AD at point R. In other words, continuous meshingof the convex tooth profile AC and the concave tooth profile AD isensured. In addition, the meshing begins from the position where point Cmakes contact with point D (state when point Q is at B) and ends withmeshing at point A (state when point Q is at A). It is thereforeso-called pass meshing.

By way of reference, FIG. 6 shows a contrasting example ofcountermovement meshing in an earlier invention of the inventor. It iswell known that pass meshing is superior from the viewpoint of retentionof lubricating oil.

FIG. 7 shows the meshing of the tooth profiles of this invention drawnrelatively with respect to one tooth space of the rigid internal gearfollowed over the passage of time. FIG. 8 shows the meshing drawnspatially over half the teeth. From FIG. 8 it can further be seen thatthe meshing region excludes the vicinity of the major axis. This, takenin light of the fact that the bending stress accompanying the ellipticaldeformation is greatest at the major axis, indicates that the presenttooth profile is also superior in the aspect of maintaining rimstrength.

Next, the properties of a flexible external gear with respect to coningwill be considered. The tooth profile of this invention is derived fromthe moving path of the basic section and does not apply to othersections without modification. This is shown in FIG. 9. FIG. 9(a) showsthe meshing at a section on the opening side of the basic section and(c) shows the meshing at a section on the diaphragm side of the basicsection.

From these figures it can be seen that in a section on the diaphragmside of the basic section, there is no danger interference owing to theoccurrence of a gap between the two tooth profiles. In contrast, it canbe seen that interference occurs between the teeth in a section on theopening side of the basic section. As shown in FIG. 10(a), therefore,this invention concurrently uses a method which avoids interference andbrings the meshing closer to normal by applying relieving matched to theamount of tooth interference on the opening side of the basic section.FIG. 9(b) shows the meshing at the section on the opening side when thisrelieving is applied.

While the situation is acceptable without modification in a section onthe diaphragm side of the basic section, it is also possible, as shownin FIG. 10(b), to positively expand the meshing region by furtherapplying reverse relieving matched to the amount of tooth clearance ondiaphragm side of the basic section. FIG. 9(d) shows the meshing of thesection in this case.

An example of the application of this invention to the tooth profiles ofa flexible meshing type gear device fitted with a cup-shaped flexibleexternal gear was explained in the foregoing. This invention can,however, also be applied to the tooth profiles of a flexible meshingtype gear device fitted with a flexible external gear of so-calledflat-type annular shape and not requiring any consideration regardingconing. Since in this case there is no need to consider interference orthe like of the two gears because of coning, relieving of the typedescribed above is unnecessary.

Industrial Applicability

By the present invention, it is possible to greatly enhance the abilityto retain a lubricating oil film between the tooth surfaces and tomarkedly improve the permissible transmitted torque of the flexiblemeshing type gear device based on tooth surface wear. By eliminating thevicinity of the major axis of the flexible external gear from themeshing range, moreover, an improvement in the rim strength of theflexible external gear can be achieved.

In addition, when this invention is applied to a device equipped with acup-shaped flexible external gear, it can be applied independently ofthe coning angle of the flexible external gear. As a result, theinvention has the merit of being applicable without modification totypes having cup-shaped flexible external gears of short body length.

We claim:
 1. A flexible meshing type gear device with a pass meshingtooth profile having a rigid internal gear, a flexible external gearinside the internal gear and a wave generator for flexing the externalgear into an elliptical cross-sectional shape, causing the external gearto mesh partially with the rigid internal gear and rotating the meshposition of the two gears in the circumferential direction, rotation ofthe wave generator producing relative rotation between the two gears,the flexible meshing type gear device with a pass meshing tooth profilebeing characterized in that(a) the rigid internal gear and the flexibleexternal gear are both spur gears, (b) the number of teeth of theflexible external gear is two greater than that of the rigid internalgear, (c) the tooth profile of the flexible external gear is convex andthe shape thereof is that of a curve obtained by subjecting a movingpart portion which, at a moving path that the external gear describesrelative to the internal gear, as determined by rack approximation, isconvex relative to the internal gear, to similarity transformation at areduction ratio λ using a limiting point of the contact between the twogears on the path as an origin, and (d) the tooth profile of the rigidinternal gear is concave and the shape thereof is that of a curveobtained by subjecting the same portion convex relative to the internalgear at the moving path to similarity transformation at an enlargementratio (1+λ) using the limiting point as the origin, whereby the meshingof the two gears maintains continuous contact and is of the passingtype.
 2. Flexible meshing type gear device with a pass meshing toothprofile having a rigid internal gear, a cup-shaped flexible externalgear inside the internal gear, and a wave generator for flexing theexternal gear into an elliptical cross-sectional shape such that anamount of deflection produced in a deflected portion of the externalgear increases from a diaphragm side thereof toward an opening portionthereof approximately in proportion to a distance from the deflectedportion to the diaphragm, causing the external gear to mesh partiallywith the rigid internal gear and rotating the mesh position of the twogears in the circumferential direction, rotation of the wave generatorproducing relative rotation between the two gears, the flexible meshingtype gear device with a pass meshing tooth profile being characterizedin that(a) the rigid internal gear and the cup-shaped flexible externalgear are both spur gears, (b) the number of teeth of the cup-shapedflexible external gear is two greater than that of the rigid internalgear, (c) the tooth profile of the cup-shaped flexible external gear isconvex and the shape thereof is that of a curve obtained by subjecting amoving path portion which, at a moving path that the external geardescribes relative to the internal gear in a basic section of the toothtrace, as determined by rack approximation, is convex relative to theinternal gear, to similarity transformation at a reduction ratio λ usinga limiting point of the contact between the two gears on the path as anorigin, (d) the tooth profile of the rigid internal gear is concave andthe shape thereof is that of a curve obtained by subjecting the sameportion convex relative to the internal gear at the moving path tosimilarity transformation at an enlargement ratio (1+λ) using thelimiting point as the origin, whereby the meshing of the two gearsmaintain continuous contact and is of the passing type, and (e)relieving is applied to teeth of the cup-shaped flexible external geartoward the opening side from the basic section of the tooth trace.
 3. Aflexible meshing type gear device with passing tooth profile accordingto claim 2, wherein reverse relieving is applied to teeth of thecup-shaped flexible external gear toward the diaphragm side from thebasic section of the tooth trace.